Data analysis
affects practical decisions. It involves construction of hypotheses and testing them. The 2-sided test covers both p_{1}
> p_{2} and p_{2} > p_{1}. The 1-sided test covers either p_{1} > p_{2 }or
p_{2} > p_{1} and not both. The 2-sided test is preferentially used because it is more conservative. Simple
manual inspection of the data is needed can help identify outliers, assess the normality of data, identify commonsense relationships,
and alert the investigator to errors in computer analysis. Data models for continuous data can be straight line regression,
non-linear regression, or trends. Data models for categorical data are the maximum likelihood and the logistic models. Two
procedures are employed in analytic epidemiology: test for association and measures of effect. The test for association is
done first. The assessment of the effect measures is done after finding an association. Effect measures are useless in situations
in which tests for association are negative. The common tests for association are: t-test, F test, chi-square, the linear
correlation coefficient, and the linear regression coefficient. The effect measures commonly employed are: Odds Ratio, Risk
Ratio, Rate difference. Measures of trend can discover relationships that are too small to be picked up by association and
effect measures.

TESTS OF ASSOCIATION

The tests of association for continuous data are the t-test, the F-test, the correlation coefficient, and the regression
coefficient. The t-test is used for two sample means. Analysis of variance, ANOVA (F test) is used for more than 2 sample
means. 1-way ANOVA involves one factor (explanatory variable). 2-way ANOVA involves 2 factors. Multiple analysis of variance,
MANOVA, is used to test for more than 2 factors. Linear regression is used in conjunction with the t test for data that requires
modeling. Dummy variables in the regression model can be used to control for confounding factors like age and sex.

The common test of association for discrete data is the chi square test. The chisquare test is used to test association
of 2 or more proportions in contingency tables. The exact test is used to test proportions for small sample sizes. The Mantel-Haenszel
chi-square statistic is used to test for association in stratified 2 x 2 tables. The chi square statistic is valid in one
of the following conditions: (a) if at least 80% of cells have more than 5 observed (b) if at least 80% of cells have more
than 1.0 expected, (c) if there are at least 5 observed in 80% of cells. If the observations are not independent of one another
as in paired or matched studies, the McNemar chisquare test is used instead of the usual Pearson chisquare test. The chisquare
works best for approximately Gaussian distributions.